The present invention generally relates to image processing. More specifically, the present invention relates to systems and methods for computer vision using curvelets.
Curvelets are a recent construction of a transform with excellent time-frequency-orientation localization. Curvelets are a tight frame of L2  Each function fεL2  has the representation:f=Σf,φj,l,kφj,l,k 
where j≧0 is the scale index, lε[0,2π] is the orientation index and kε2 is the location. In addition, the Parseval equality holds:
                  f              2    2    =            ∑              j        ,        l        ,        k              ⁢                                    〈                      f            ,                          φ                              j                ,                l                ,                k                                              〉                            2      
Curvelet functions at the scale j=0 are of a different nature, exactly as in the Fourier and wavelets transforms, and their role is to capture a low-resolution approximation of the function. From the scale j=1 through to higher scales, the essential support of the curvelet functions becomes longer and thinner.
An exemplary implementation of a curvelet transform is discussed in United States Patent Application Publication Number 2007/0038691, entitled “Methods for Performing Fast Discrete Curvelet Transforms of Data.”